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In physics, the Tsallis entropy is a generalization of the standard Boltzmann-Gibbs entropy. It was an extension put forward by Constantino Tsallis in 1988. It is defined as
Additional recommended knowledge
or in the discrete case
In this case, p denotes the probability distribution of interest, and q is a real parameter. In the limit as q → 1, the normal Boltzmann-Gibbs entropy is recovered.
The parameter q is a measure of the non-extensitivity of the system of interest. There are continuous and discrete versions of this entropic measure.
The discrete Tsallis entropy satisfies
where Dq is the q-derivative.
Given two independent systems A and B, for which the joint probability density satisfies
the Tsallis entropy of this system satisfies
From this result, it is evident that the parameter q is a measure of the departure from extensivity. In the limit when q = 1,
which is what is expected for an extensive system.
Categories: Entropy and information | Thermodynamic entropy
|This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Tsallis_entropy". A list of authors is available in Wikipedia.|